System and methods for intrinsic reward reinforcement learning

ABSTRACT

A learning agent is disclosed that receives data in sequence from one or more sequential data sources; generates a model modelling sequences of data and actions; and selects an action maximizing the expected future value of a reward function, wherein the reward function depends at least partly on at least one of: a measure of the change in complexity of the model, or a measure of the complexity of the change in the model. The measure of the change in complexity of the model may be based on, for example, the change in description length of the first part of a two-part code describing one or more sequences of received data and actions, the change in description length of a statistical distribution modelling, the description length of the change in the first part of the two-part code, or the description length of the change in the statistical distribution modelling.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional PatentApplication No. 62/351,313, entitled “System and Method for IntrinsicReward Reinforcement Learning,” filed Jun. 17, 2016, the entirety ofwhich is hereby incorporated by reference.

BACKGROUND: FIELD OF THE INVENTION

The invention pertains to a system and methods for reinforcementlearning, and, in particular, intrinsically motivated reinforcementlearning.

BACKGROUND: RELATED ART

Reinforcement learning is a category of machine learning in which amachine (agent) learns a policy specifying which action to take in anysituation (state), in order to maximize the expected reward according toa reward function. Reinforcement learning methods typically compute avalue function expressing the expected longer term reward of a state,and may also compute a predictive model of the environment in terms ofsequences of states, actions, and rewards. While powerful, reinforcementlearning agents are dependent on the crafting of an appropriate rewardfunction towards some task or goal, for example scoring points in agame, and are further dependent on hand-tuned parameters controllinglearning rates, future reward discount factors, and exploit-vs-exploretrade-offs. Natural learning agents, such as humans, apparently do notsuffer from such limitations.

Q Learning is a reinforcement learning method that does not explicitlyconstruct a predictive model of the environment. Instead, it directlycomputes a value function called a Q function, which in its simplestform is represented as a table that maps state-action pairs to expectedvalue. Table representations do not scale to large domains, so functionapproximations are often employed including convolutional neuralnetworks. Q learning suffers from slow convergence compared tomodel-based methods, which is typically mitigated using so-calledexperience replay, which samples sequences of states that werepreviously encountered and stored in a replay memory. The replay memoryitself effectively serves as a predictive model of the environment,based on discrete sampling. While Q Learning has received much attentionin recent works, none address the issue of designing general rewardfunctions.

The concept of intrinsic motivation has been introduced intoreinforcement learning in an effort to enable an agent to learn aspectsof the environment not directly related to a specific goal, throughself-guided exploration. Typical intrinsic motivation techniques rewardexploration of states that are not well predicted by the model, orreward increased reliability in predictions which is sometimes referredto as progress. While these methods show some promise, an agent that isdriven to explore and model every last minutia of its environment is notlikely to perform effectively in highly complex domains.

SUMMARY

The following summary is included in order to provide a basicunderstanding of some aspects and features of the invention. Thissummary is not an extensive overview of the invention and as such it isnot intended to particularly identify key or critical elements of theinvention or to delineate the scope of the invention. Its sole purposeis to present some concepts of the invention in a simplified form as aprelude to the more detailed description that is presented below.

A solution for reinforcement learning using an intrinsic reward functionthat requires no task-specific programming, and instead rewards the actof learning itself. In essence, learning is its own reward. Such afunction may be employed to drive a general agent, or may be used incombination with a task-specific reward function as an alternative toad-hoc exploit-vs-explore heuristics. The main feature of the inventionthat sets it apart from previous intrinsically motivated learning agentsis a reward function based on the change in the complexity of thelearned model, or the complexity of the change of the learned model, orboth, optionally in combination with a task-specific reward, andoptionally in combination with traditional intrinsic motivation rewardssuch as rewarding the accuracy of the model. Intuitively, encouraginglarge changes in the complexity of the learned model will encourage theagent to maximize its knowledge. We propose several measures ofcomplexity that measure structure in the model while ignoring noise inthe observed data, so that the agent is rewarded for discovering morecomplex structures, and not rewarded for simply finding more data.Further, encouraging more complex changes in the learned model willencourage the agent to challenge its own understanding of the data,which may help prevent the agent from becoming obsessed with a subset ofdata containing a great deal of structure.

A learning agent may receive data in sequence from one or moresequential data sources; generate a model modelling sequences of dataand actions; and select an action maximizing the expected future valueof a reward function, wherein the reward function depends at leastpartly on at least one of: a measure of the change in complexity of themodel, or a measure of the complexity of the change in the model. Theagent may be trained using any reasonable reinforcement learningtechnique, for example Q Learning with experience replay, or deepreinforcement learning.

Any reasonable measure of the change in complexity of the model may beemployed, but those that measure structure while ignoring noise areadvantageous. For example, the measure of the change in complexity ofthe model may be based on the change in description length or,equivalently, the change in negative log likelihood, of the first partof a two-part code describing one or more sequences of received data andactions, Alternatively, the measure of the change in complexity of themodel may be based on the change in description length or, equivalently,the change in negative log likelihood, of a statistical distributionmodelling one or more sequences of received data and actions.

Likewise, any reasonable measure of the complexity of the change in themodel may be employed, but those that measure structure while ignoringnoise are advantageous. For example, the measure of the complexity ofthe change in the model may be based on the description length or,equivalently, the negative log likelihood, of the change in the firstpart of a two-part code describing one or more sequences of receiveddata and actions. Alternatively, the measure of the complexity of thechange in the model may be based on the description length or,equivalently, the negative log likelihood, of the change in astatistical distribution modelling one or more sequences of receiveddata and actions.

The representation of the model may take any form that is useful forpredicting or synthesizing sequences of data and actions, which may beused to generate training samples for the reinforcement learningalgorithm. Examples include: a neural network that approximatelypredicts sequences of received data and actions; a replay memory thatstores sequences of received data and actions; or a statisticaldistribution factorized into potential functions over cliques on afactor graph containing nodes corresponding to the data sources as wellas zero or more additional nodes corresponding to auxiliary variables.

The description length of a factor graph model may be computed as thesum of description length of the graph structure and the descriptionlengths of the potential functions defined over cliques on the graph.The description length of commonly occurring potential functions may bediscounted, and the description length of commonly occurring subgraphsin the factor graph may be discounted. Indeed any reasonable compressedgraph representation may be adapted to include clique potentials andemployed in computing the description length.

A potential function associated with a clique defined in a factor graphmay be conditioned on a conditioning value at each node in the clique.The conditioning value at a node may come from the data sourceassociated with the node (if any); a random value; or a maximumlikelihood value estimated from the factor graph with potentialfunctions conditioned on another, possibly different, set ofconditioning values, for example from a previous point in time. Thisallows the potential functions to be conditioned on the data, and alsoenables the factor graph to represent temporal structure.

Maximum likelihood values and marginal distributions at the factor graphnodes may be employed to generate data for training the reinforcementlearning, and may be estimated using any reasonable factor graphinference algorithm. The potential functions may be learned using anyreasonable factor graph learning algorithm.

In accordance with one aspect of the invention, a system, method andcomputer readable medium are disclosed for reinforcement learning thatperform actions from a set of available actions; receive data insequence from one or more sequential data sources; generate a model thatmodels sequences of the received data and the performed actions; andselect an action to maximize an expected future value of a rewardfunction, wherein the reward function depends at least partly on atleast one of: a measure of a change in complexity of the model or ameasure of the complexity of the change in the model.

The measure of the change in complexity of the model may be based on achange in description length of the first part of a two-part codedescribing one or more sequences of received data and actions.

The measure of the change in complexity of the model may be based on achange in negative log likelihood of the first part of a two-part codedescribing one or more sequences of received data and actions.

The measure of the complexity of the change in the model may be based ona description length of a change in a first part of a two-part codedescribing one or more sequences of received data and actions.

The measure of the complexity of the change in the model may be based ona negative log likelihood of a change in a first part of a two-part codedescribing one or more sequences of received data and actions.

The measure of the change in complexity of the model may be based on achange in description length of a statistical distribution modelling oneor more sequences of received data and actions.

The measure of the change in complexity of the model may be based on achange in negative log likelihood of a statistical distributionmodelling one or more sequences of received data and actions.

The measure of the complexity of the change in the model may be based ona description length of a change in a statistical distribution modellingone or more sequences of received data and actions.

The measure of the complexity of the change in the model may be based ona negative log likelihood of a change in a statistical distributionmodelling one or more sequences of received data and actions.

The model may be represented as a neural network that approximatelypredicts sequences of received data and actions.

The model may be represented as a replay memory that stores sequences ofreceived data and actions, and an action is at least sometimes selectedaccording to an action-value function learned via Q Learning withexperience replay.

The model may be represented as a statistical distribution factorizedinto potential functions over cliques on a factor graph containing nodescorresponding to the data sources as well as zero or more additionalnodes corresponding to auxiliary variables.

A first potential function may be similar to a second potential functionwhen variables in the first potential function are substituted forvariables in the second potential function, and the complexity of themodel may be reduced by the second potential function referencing thefirst potential function or by the first and second potential functionsreferencing a common function.

A potential function over a clique may be conditioned on a conditioningvalue at each node in the clique, where the conditioning value at eachnode may be one of: a data value received from a data source associatedwith the node; a random value; or a maximum likelihood value estimatedfrom the factor graph with potential functions conditioned on anotherset of conditioning values.

The another set of conditioning values are different from a previouspoint in time.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and constitute apart of this specification, illustrate one or more examples ofembodiments and, together with the description of example embodiments,serve to explain the principles and implementations of the embodiments.

FIG. 1 is a diagram of a system in accordance with one embodiment of theinvention.

FIG. 2 illustrates a computer connected to one or more data sources inaccordance with one embodiment of the invention.

FIG. 3 is a flowchart illustrating a method in accordance with oneembodiment of the invention.

DETAILED DESCRIPTION

Embodiments of the invention are directed to a learning agent thatreceives data in sequence from one or more sequential data sources;generates a model modelling sequences of data and actions; and selectsan action maximizing the expected future value of a reward function,wherein the reward function depends at least partly on at least one of:a measure of the change in complexity of the model, or a measure of thecomplexity of the change in the model. The measure of the change incomplexity of the model may be based on the change in description lengthof the first part of a two-part code describing one or more sequences ofreceived data and actions, or the change in description length of astatistical distribution modelling one or more sequences of receiveddata and actions. The measure of the complexity of the change in themodel may be based on the description length of the change in the firstpart of a two-part code describing one or more sequences of receiveddata and actions, or the description length of the change in astatistical distribution modelling one or more sequences of receiveddata and actions. The representation of the model may be a neuralnetwork that approximately predicts sequences of received data andactions, a replay memory that stores sequences of received data andactions, or a statistical distribution factorized into potentialfunctions over cliques on a factor graph containing nodes correspondingto the data sources as well as zero or more additional nodescorresponding to auxiliary variables. The description length may bediscounted for commonly occurring potential functions, and for subgraphsthat are isomorphic to other. A potential function associated with aclique may be conditioned on a set of conditioning values, which maycome from the data sources, random valued; or maximum likelihood valuedestimated from the factor graph with potential functions conditioned onanother, possibly different, set of conditioning values.

Examples of applications of the reinforcement learning agent systems andmethods disclosed herein include computer opponent for games andentertainment, elevator control, job scheduling, cellular device channelallocation, robot control, supply chain management and the like. Inaddition, the reinforcement learning agent systems and methods disclosedherein may be combined with the systems and methods for suggestingbeneficial actions disclosed in U.S. application Ser. No. 15/477,959,filed Apr. 3, 2017, the entirety of which is hereby incorporated byreference. It will be appreciated that there are numerous otherapplications of the reinforcement learning systems and methods describedherein as understood by those of skill in the art.

FIG. 1 shows a reinforcement learning system 100 in accordance with oneembodiment of the invention. The reinforcement learning system 100includes sequential data 105, a predictive model 115, a set of actions125, sequences of data and actions 120, and a reward function 130.

The system 100 receives the sequential data 105 from one or moresequential data sources 110. The data 105 may relate to an environment135. Examples of data sources 110 include: pixel values from an imagesensor, audio sample values from a microphone, characters in a textstream, telemetry values from a motor system with feedback, image ortext media output from a computer application, media data obtained fromthe internet, or the like.

The system 100 generates the predictive model 115, which models thesequences 120, as discussed in further detail below.

The system 100 selects an action 125 maximizing the expected futurevalue of a reward function 130. Examples of actions 125 the system mayselect include outputting signals to drive a motor, outputting audiosamples to a speaker, outputting pixel values to a display, outputtingtext characters to drive a speech synthesis device, inputting commandsto a computer application, retrieving a media file from the internet, orthe like. The reward function 130 depends at least partly on at leastone of: a measure of the change in complexity of the model 115, or ameasure of the complexity of the change in the model 115. The system 100may perform the selected action 125 and the action 125 may have aneffect on the environment 135.

The system 100 may be trained using any reasonable reinforcementlearning technique. In general, the model 115 of sequences 120 ofreceived data and actions may be constructed based on the data 105received by the system and the actions 125 selected by the system,independent of the choice of reinforcement learning technique. It willbe appreciated that some reinforcement techniques already include amodel; in such cases, the model included in the reinforcement techniquemay be employed as the model 115 for the purposes of computing thereward function 130. To compute the reward function 130, any reasonablemeasure of the change in complexity of the model 115 may be employed,and any reasonable measure of the complexity of the change in the model115 may be employed, but those that measure structure while ignoringnoise are advantageous. The representation of the model 115 may take anyform that is useful for predicting or synthesizing sequences 120 of dataand actions, which may be employed to train the reinforcement learningalgorithm.

FIG. 2 depicts a computer 205 connected to one or more data sources 110and a network 225. In one embodiment, the reinforcement learning system100 includes the computer 205 connected to the network 225. The computer205 is configured with one or more processors 210, a memory 215, and oneor more network controllers 220. It is understood that the components ofthe computer 205 are configured and connected in such a way as to beoperational, so that an operating system and application programs mayreside in the memory 215 and may be executed by the processor orprocessors 210 and data may be transmitted or received via the networkcontroller 220 according to instructions executed by the processor orprocessors 210. In one embodiment, a data source 110 may be connected tothe system 100 remotely via the network 225, for example in the case ofmedia data obtained from the Internet. In one embodiment, a data source110 may be connected directly to the computer 205 and accessible to theprocessor 210, for example in the case of an imaging sensor, telemetrysensor, or the like. Those skilled in the art will appreciate that theone or more processors 210, memory 215, or network controllers 220 mayphysically reside on multiple physical components within the computer205, or may be integrated into fewer physical components within thecomputer 205, without departing from the scope of the invention. In oneembodiment, a plurality of computers 205 may be configured to executesome or all of the steps listed herein, such that the cumulative stepsexecuted by the plurality of computers are in accordance with theinvention.

FIG. 3 shows a flowchart in accordance with one or more embodiments ofthe invention. It is understood by those skilled in the art that somesteps are optional, and some steps may be performed in a differentsequence, without departing from the scope of the invention. In STEP305, sequential data 105 is received from one or more sequential datasources 110 where the data 105 may relate to an environment 135. In STEP310, a predictive model 115 is generated that models sequences 120 ofdata and actions. In STEP 315, an action 125 is selected to maximize theexpected future value of a reward function 130, wherein the rewardfunction 130 depends at least partly on at least one of: a measure ofthe change in complexity of the model 115, or a measure of thecomplexity of the change in the model 115. In STEP 320, the selectedaction 125 may be performed, and may have an effect on the environment135.

In one embodiment, a computer 205 is configured to execute instructionsto: receive sequential data 105 from one or more sequential data sources110 where the data 105 may relate to an environment 135; generate apredictive model 115 that models sequences 120 of data and actions;select an action 125 to maximize the expected future value of a rewardfunction 130, wherein the reward function 130 depends at least partly onat least one of: a measure of the change in complexity of the model 115,or a measure of the complexity of the change in the model 115; andperform the selected action 125, which may have an effect on theenvironment 135. Data 105 may be transmitted from a data source 110 to acomputer 205 via a computer network 225. Data 105 may also be accessedby the computer 205 from a data source 110 connected to the computer205. It is understood by those skilled in the art that some steps areoptional, and some steps may be performed in a different sequence,without departing from the scope of the invention. A computer readablemedium may store instructions for performing the steps listed herein.

In one embodiment, the measure of the change in complexity of the model115 may be based on the change in description length or, equivalently,the change in negative log likelihood, of the first part of a two-partcode describing one or more sequences 120 of received data and actions,and the measure of the complexity of the change in the model 115 may bebased on the description length or, equivalently, the negative loglikelihood, of the change in the first part of a two-part codedescribing one or more sequences 120 of received data and actions.

In one embodiment, the measure of the change in complexity of the model115 may be based on the change in description length or, equivalently,the change in negative log likelihood, of a statistical distributionmodelling one or more sequences 120 of received data and actions, andthe measure of the complexity of the change in the model 115 may bebased on the description length or, equivalently, the negative loglikelihood, of the change in a statistical distribution modelling one ormore sequences 120 of received data and actions. In one embodiment,statistical distributions belonging to the exponential family may beassigned a description length based on the negative logarithm of theJeffries prior.

In one embodiment, Q Learning with experience replay is used to trainthe system 100.

In one embodiment, deep reinforcement learning is used to train thesystem 100.

In one embodiment, the model 115 may be represented as a neural networkthat approximately predicts sequences 120 of received data and actions.In one embodiment, a model 115 represented as a neural network may beassigned a description length based on the storage requirements of acompressed representation of the neural network, for example, usingHashed Nets.

In one embodiment, the model 115 may be represented as a replay memorythat stores sequences 120 of received data and actions. In oneembodiment, a model represented as a replay memory may be assigned adescription length based on the description length of the modelparameters of a model selected using unsupervised learning based on theminimum description length principle for sequences, for example.

In one embodiment, the model 115 may be represented as a statisticaldistribution factorized into potential functions over cliques on afactor graph containing nodes corresponding to the data sources as wellas zero or more additional nodes corresponding to auxiliary variables.Potential functions may be represented as Gaussian mixture models,stochastic samples, discrete density functions, or other reasonabledensity functions.

In one embodiment, the description length of a factor graph model may becomputed as the sum of description length of the graph structure and thedescription lengths of the potential functions defined over cliques onthe graph. In one embodiment, a Gaussian mixture model may be assigned adescription length of ½M (L+1) log N, where M is the number of mixturecomponents, L is the number of parameters defining each component, and Nis the number of samples employed to construct the Gaussian mixturemodel, and the mixture components may be generated using the minimumdescription length principle. In one embodiment, density functionsbelonging to the exponential family may be assigned a description lengthbased on the negative logarithm of the Jeffries prior. In oneembodiment, the description length of commonly occurring potentialfunctions may be discounted. For example, two or more potentialfunctions present in the factor graph that differ only by variablesubstitution may reference a common function definition and store onlythe required substitutions, thereby amortizing the description lengthover the multiple potential functions. A similar concept may be appliedfor sharing only part of a potential function while other parts differ,for example sharing a subset of the components occurring in a Gaussianmixture model representation. The description length of a commonlyoccurring subgraph in the factor graph may be discounted, where thesubgraph is isomorphic to one or more other subgraphs having cliqueswith similar potential functions up to variable substitutions, which maybe implemented by referencing a common definition and the requiredvariable substitutions and graph edges connecting the subgraph to therest of the factor graph. Indeed, any reasonable compressed graphrepresentation may be adapted to include clique potentials and employedin computing the description length. In one embodiment, a potentialfunction associated with a clique may be conditioned on a conditioningvalue at each node in the clique. The conditioning value at a node maycome from the data source associated with the node (if any); a randomvalue; or a maximum likelihood value estimated from the factor graphwith potential functions conditioned on another, possibly different, setof conditioning values, for example from a previous point in time. Thisallows the potential functions to be conditioned on the data, and alsoenables the factor graph to represent temporal structure. In oneembodiment, maximum likelihood values and marginal distributions at thefactor graph nodes may be employed to generate data for training thereinforcement learning, and may be estimated using any reasonable factorgraph inference algorithm. The potential functions may be learned usingany reasonable factor graph learning algorithm.

One or more of the methodologies or functions described herein may beembodied in a computer-readable medium on which is stored one or moresets of instructions (e.g., software). The software may reside,completely or at least partially, within memory and/or within aprocessor during execution thereof. The software may further betransmitted or received over a network.

It should be understood that components described herein includecomputer hardware and/or executable software code which is stored on acomputer-readable medium for execution on appropriate computinghardware.

The terms “computer-readable medium” or “machine readable medium” shouldbe taken to include a single medium or multiple media that store the oneor more sets of instructions. The terms “computer-readable medium” or“machine readable medium” shall also be taken to include anynon-transitory storage medium that is capable of storing, encoding orcarrying a set of instructions for execution by a machine and that causea machine to perform any one or more of the methodologies describedherein. The terms “computer-readable medium” or “machine readablemedium” shall accordingly be taken to include, but not be limited to,solid-state memories, and optical and magnetic media. For example,“computer-readable medium” or “machine readable medium” may includeCompact Disc Read-Only Memory (CD-ROMs), Read-Only Memory (ROMs), RandomAccess Memory (RAM), and/or Erasable Programmable Read-Only Memory(EPROM). In other embodiments, some of these operations might beperformed by specific hardware components that contain hardwired logic.Those operations might alternatively be performed by any combination ofprogrammable computer components and fixed hardware circuit components.

While the invention has been described in terms of several embodiments,those of ordinary skill in the art will recognize that the invention isnot limited to the embodiments described, but can be practiced withmodification and alteration within the spirit and scope of the appendedclaims. The description is thus to be regarded as illustrative insteadof limiting. There are numerous other variations to different aspects ofthe invention described above, which in the interest of conciseness havenot been provided in detail. Accordingly, other embodiments are withinthe scope of the claims.

It should be understood that processes and techniques described hereinare not inherently related to any particular apparatus and may beimplemented by any suitable combination of components. Further, varioustypes of general purpose devices may be used in accordance with theteachings described herein. The present invention has been described inrelation to particular examples, which are intended in all respects tobe illustrative rather than restrictive. Those skilled in the art willappreciate that many different combinations will be suitable forpracticing the present invention.

Moreover, other implementations of the invention will be apparent tothose skilled in the art from consideration of the specification andpractice of the invention disclosed herein. Various aspects and/orcomponents of the described embodiments may be used singly or in anycombination. It is intended that the specification and examples beconsidered as exemplary only, with a true scope and spirit of theinvention being indicated by the following claims.

1. A reinforcement learning system, comprising: one or more processors;and one or more programs residing on a memory and executable by the oneor more processors, the one or more programs configured to: performactions from a set of available actions; receive data in sequence fromone or more sequential data sources; generate a model that modelssequences of the received data and the performed actions; and select anaction to maximize an expected future value of a reward function,wherein the reward function depends at least partly on at least one of:a measure of a change in complexity of the model or a measure of thecomplexity of the change in the model.
 2. The system of claim 1, whereinthe measure of the change in complexity of the model is based on achange in description length of the first part of a two-part codedescribing one or more sequences of received data and actions.
 3. Thesystem of claim 1, wherein the measure of the change in complexity ofthe model is based on a change in negative log likelihood of the firstpart of a two-part code describing one or more sequences of receiveddata and actions.
 4. The system of claim 1, wherein the measure of thecomplexity of the change in the model is based on a description lengthof a change in a first part of a two-part code describing one or moresequences of received data and actions.
 5. The system of claim 1,wherein the measure of the complexity of the change in the model isbased on a negative log likelihood of a change in a first part of atwo-part code describing one or more sequences of received data andactions.
 6. The system of claim 1, wherein the measure of the change incomplexity of the model is based on a change in description length of astatistical distribution modelling one or more sequences of receiveddata and actions.
 7. The system of claim 1, wherein the measure of thechange in complexity of the model is based on a change in negative loglikelihood of a statistical distribution modelling one or more sequencesof received data and actions.
 8. The system of claim 1, wherein themeasure of the complexity of the change in the model is based on adescription length of a change in a statistical distribution modellingone or more sequences of received data and actions.
 9. The system ofclaim 1, wherein the measure of the complexity of the change in themodel is based on a negative log likelihood of a change in a statisticaldistribution modelling one or more sequences of received data andactions.
 10. The system of claim 1, wherein the model is represented asa neural network that approximately predicts sequences of received dataand actions.
 11. The system of claim 1, wherein the model is representedas a replay memory that stores sequences of received data and actions,and an action is at least sometimes selected according to anaction-value function learned via Q Learning with experience replay. 12.The system of claim 1, wherein the model is represented as a statisticaldistribution factorized into potential functions over cliques on afactor graph containing nodes corresponding to the data sources as wellas zero or more additional nodes corresponding to auxiliary variables.13. The system of claim 12, wherein a first potential function issimilar to a second potential function when variables in the firstpotential function are substituted for variables in the second potentialfunction, and the complexity of the model is reduced by the secondpotential function referencing the first potential function or by thefirst and second potential functions referencing a common function. 14.The system of claim 12, wherein a potential function over a clique isconditioned on a conditioning value at each node in the clique, wherethe conditioning value at each node is one of: a data value receivedfrom a data source associated with the node; a random value; or amaximum likelihood value estimated from the factor graph with potentialfunctions conditioned on another set of conditioning values.
 15. Thesystem of claim 14, wherein the another set of conditioning values aredifferent from a previous point in time.
 16. A method for reinforcementlearning, comprising the steps of: receiving data in sequence from theone or more sequential data sources; generating a model, wherein themodel is configured to model sequences of the received data and actions;and selecting an action maximizing the expected future value of a rewardfunction, wherein the reward function depends at least partly on atleast one of: a measure of the change in complexity of the model, or ameasure of the complexity of the change in the model.
 17. The method ofclaim 16, wherein the measure of the change in complexity of the modelis based on a change in description length of the first part of atwo-part code describing one or more sequences of received data andactions.
 18. The method of claim 16, wherein the measure of the changein complexity of the model is based on a change in negative loglikelihood of the first part of a two-part code describing one or moresequences of received data and actions.
 19. The method of claim 16,wherein the measure of the complexity of the change in the model isbased on a description length of a change in a first part of a two-partcode describing one or more sequences of received data and actions. 20.The method of claim 16, wherein the measure of the complexity of thechange in the model is based on a negative log likelihood of a change ina first part of a two-part code describing one or more sequences ofreceived data and actions.
 21. The method of claim 16, wherein themeasure of the change in complexity of the model is based on a change indescription length of a statistical distribution modelling one or moresequences of received data and actions.
 22. The method of claim 16,wherein the measure of the change in complexity of the model is based ona change in negative log likelihood of a statistical distributionmodelling one or more sequences of received data and actions.
 23. Themethod of claim 16, wherein the measure of the complexity of the changein the model is based on a description length of a change in astatistical distribution modelling one or more sequences of receiveddata and actions.
 24. The method of claim 16, wherein the measure of thecomplexity of the change in the model is based on a negative loglikelihood of a change in a statistical distribution modelling one ormore sequences of received data and actions.
 25. The method of claim 16,wherein the model is represented as a neural network that approximatelypredicts sequences of received data and actions.
 26. The method of claim16, wherein the model is represented as a replay memory that storessequences of received data and actions, and an action is at leastsometimes selected according to an action-value function learned via QLearning with experience replay.
 27. The method of claim 16, wherein themodel is represented as a statistical distribution factorized intopotential functions over cliques on a factor graph containing nodescorresponding to the data sources as well as zero or more additionalnodes corresponding to auxiliary variables.
 28. The method of claim 27,wherein a first potential function is similar to a second potentialfunction when variables in the first potential function are substitutedfor variables in the second potential function, and the complexity ofthe model is reduced by the second potential function referencing thefirst potential function or by the first and second potential functionsreferencing a common function.
 29. The method of claim 27, wherein apotential function over a clique is conditioned on a conditioning valueat each node in the clique, where the conditioning value at each node isone of: a data value received from a data source associated with thenode; a random value; or a maximum likelihood value estimated from thefactor graph with potential functions conditioned on another set ofconditioning values.
 30. The method of claim 29, wherein the another setof conditioning values are different from a previous point in time.